A strongly-consistent difference scheme for 3D nonlinear Navier-Stokes equations

DOI10.1007/s11424-020-9325-3zbMath1483.65144OpenAlexW3119006678MaRDI QIDQ2121178

Yu-Fu Chen, Xiao-Jing Zhang

Publication date: 1 April 2022

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-020-9325-3

zbMATH Keywords

Navier-Stokes equationssymbolic computationfinite difference schemedifference algebradifference Gröbner basis

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Navier-Stokes equations (35Q30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Uses Software

• LDA
• TDDS

Cites Work

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• Formal algorithmic elimination for PDEs
• Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals
• Involutive characteristic sets of algebraic partial differential equation systems
• Involutive bases of polynomial ideals
• Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations
• A strongly consistent finite difference scheme for steady Stokes flow and its modified equations
• Algebraic construction of a strongly consistent, permutationally symmetric and conservative difference scheme for 3D steady Stokes flow
• Difference algebra
• On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
• Gröbner bases and gradings for partial difference ideals
• The Maple package TDDS for computing Thomas decompositions of systems of nonlinear PDEs

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